Typically, in gas and liquid chromatography, experimental spectra have background features in addition to the signal of interest. One common source of background features is slow desorption of strongly adsorbed substances previously passed through a column. Baseline drift may also occur in gradient chromatography, particularly when using ultraviolet detection at short wavelengths, because absorbancies of respective solvents begin to change. Other sources of baseline instability are fluctuations in temperature of the column and/or the detector.
Baseline removal is important for applications that involve quantitation, like estimating the amount of each of the compounds generating peaks in the signal. Baseline removal is also important for numerical processing applications performed prior to quantitation, such as estimating the number of peaks present in a signal. Background removal is not only necessary in chromatography, but it is also required to interpret signals in mass spectrometry, for example.
FIG. 1A is a graph showing a signal curve 110 along with a baseline curve 120, and FIG. 1B shows the signal curve 115 with the baseline removed. Referring to FIG. 1A, it is apparent that the baseline curve 120 changes over a longer time frame than the peaks of the signal curve 110. In differential geometry terms, baselines generally are smoother than peaks, as can be seen in FIG. 1A. Therefore, in order to estimate the baseline of a signal, as is necessary, e.g., to determine the amplitudes of the peaks, the smoothness of the baseline curve 120 must be reconciled with the accuracy (or fidelity) with which the base line curve 120 matches the signal curve 110. In other words, the lower bound of the signal curve 110 should be followed as closely as possible without overestimating the baseline curve 120, especially when peaks of the signal curve 110 have a high degree of overlap.
FIG. 2 is a graph showing a signal curve 210 along with an overestimated baseline curve 220, for example, according to a conventional method for baseline estimation. The estimated baseline curve 220 of FIG. 2 is less smooth and follows the signal curve 210 more closely than the baseline curve 120 of FIG. 1A. The asterisks on the baseline curve 220 show instances in which overfitting leads to inaccurate quantitation of the peak areas of the signal curve 210.
Conventionally, digital filters have been used for automated baseline estimation, particularly with respect to periodic signals, such as electrocardiograms. However, use of digital filters tends to introduce artifacts and deform the signal. Another approach to automated baseline estimation is to assume a specified function, usually a polynomial of a certain degree, and to fit the specified function to the signal. However, an actual baseline usually does not mimic a polynomial or a small set of functions from which a user is able to choose.